The known methods for detecting magnetic abnormalities in a environment are based on a technique of inversion of a matrix, the dimensions of which depend on the pitch of a measuring grid (in the context of a reading of the total magnetic field) or on a technique of interpreting a map issuing from prospecting by a skilled man (in the context of a reading of the vertical magnetic field gradient). These known methods are detailed below.
In the context of total magnetic field (the definition of which is stated below), there exist first techniques that make it possible to transform the inverse magnetism problem into a linear system by means of hypotheses. These first techniques lead to the obtaining of a matrix describing the system that it is necessary to invert.
The matrix describing the system is linked to the pitch (the distance between two consecutive points) of a measuring grid. The conditioning of this matrix reacts as the pitch of the grid to a power proportional to the size of the grid. If this power is large, the conditioning tends abruptly towards zero as soon as the pitch of the grill passes a threshold substantially in the same way as the graph of the function f(x)=xn for n large close to the real number 1.
The transformation of the inverse problem into a linear system gives an unconvincing result because of the poor conditioning of the error. This is because these first techniques do not provide any systematic check of the error after each calculation step.
Thus these first techniques are imprecise.
In the case of the vertical gradient of the magnetic field (the definition of which is stated below), there exist second known techniques that are limited to estimating the graphical aspect of a map issuing from prospecting. Thus these second techniques lead to the conclusion that the abnormalities that have a small footprint and a high contrast on the map are abnormalities close to the surface and that the abnormalities that have a large footprint and low contrast on the map are deep abnormalities.
These second conventional techniques do not allow three-dimensional location of a magnetic object and are very imprecise.
In addition none of the aforementioned first and second techniques makes it possible to determine both the three-dimensional location and the susceptibility of a magnetic object.